Effect of Surface Modes on the Six-Dimensional Molecule–Surface Scattering Dynamics of H₂–Cu(100) and D₂–Cu(111) Systems

Abstract

We include the phonon modes originating from the three layers of Cu(100)/Cu(111) surface atoms on the dynamics of molecular [H(2)(v,j)/D(2)(v,j)] degrees of freedom (DOFs) through a mean field approach, where the surface temperature is incorporated into the effective Hamiltonian (potential) either by considering Boltzmann probability (BP) or by including the Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes. The formulation of effective potential has been carried out by invoking the expression of transition probabilities for phonon modes known from the "stochastic" treatment of linearly forced harmonic oscillator (LFHO). We perform four-dimensional (4D⊗2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time and temperature-dependent effective Hamiltonian to calculate elastic/inelastic scattering cross-section of the scattered molecule for the H(2)(v,j)-Cu(100) system, and dissociative chemisorption-physisorption for both H(2)(v,j)-Cu(100) and D(2)(v,j)-Cu(111) systems. Calculated sticking probabilities by either 4D⊗2D or 6D quantum dynamics on an effective potential constructed by using BP factor for the initial state distribution of the phonon modes could not show any surface temperature dependence. In the BEP case, (a) both 4D⊗2D and 6D quantum dynamics demonstrate that the phonon modes of the Cu(100) surface affect the state-to-state transition probabilities of the scattered H(2) molecule substantially, and (b) the sticking probabilities due to the collision of H(2) on Cu(100) and D(2) on Cu(111) surfaces show noticeable and substantial change, respectively, as function of surface temperature only when the quantum dynamics of all six molecular DOFs are treated in a fully correlated manner (6D).

Vibrational deexcitation and rotational excitation of H2 and D2 scattered from Cu(111): Adiabatic versus non-adiabatic dynamics

“…Thus, the question why experimentally the probability for H 2 (v i = 1, J i = 1) → H 2 (v f = 1, J f ) was found to be less than 1, at low energy, remains an open question. At this point, we should also point out that, although it has been suggested that survival and rotational excitation probabilities for H 2 (v i = 1, J i = 0)/Cu(111) are almost independent of surface temperature, 45 quantitative agreement with experiment may require quantum calculations beyond the static surface approximation for the same face of copper as used in the experiments.…”

“…This is the case, for example, for H 2 /Cu(100). 43 The influence of surface temperature on vibrationally inelastic scattering has also been studied experimentally 44 and theoretically, 45 suggesting small effects of surface temperature, and therefore, an adiabatic mechanism. On the other hand, Sitz and co. 46 have found that a significant amount of energy in H 2 is lost to the surface upon scattering from Cu(100).…”

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

“…In the ab initio molecular dynamics (AIMD) method the fitting of a high-dimensional PES is avoided, and instead the forces are calculated on the fly. 117,[153][154][155] With this approach there is no correlation between the molecular and lattice motion: at each instance the wave packet describing the molecule only sees an average over the moving surface atoms (i.e., the wave function describing the lattice motion). 141,142 The use of this method to study problems for which surface motion may be relevant has become increasingly popular.…”

“…139 Calculations on methane interacting with Ni (111) and Pt (111) suggest that a reasonable accuracy is available with this method. 117,[153][154][155] An advantage of these force fields is that MD calculations using such force fields are usually computationally much less expensive than AIMD calculations, while force field methods in principle allow one to model molecules interacting with thermally distorted surfaces and pre-covered surfaces. 117,[153][154][155] An advantage of these force fields is that MD calculations using such force fields are usually computationally much less expensive than AIMD calculations, while force field methods in principle allow one to model molecules interacting with thermally distorted surfaces and pre-covered surfaces.…”

Reactive scattering of H2 from Cu(100): Comparison of dynamics calculations based on the specific reaction parameter approach to density functional theory with experiment

“…48 Finally, more recently the system has been used to explore the applicability of a mean field quantum dynamics method to investigate the effect of phonons on reactive and non-reactive scattering of H 2 from copper surfaces. 49,50 Here, we present new results of energy resolved rovibrational state selective associative desorption experiments on H 2 desorbing from Cu(100) at a surface temperature (T s ) of 1030 K. An interpretation based on detailed balance allows information to be extracted on the effect of the initial rovibrational state and reagent angular momentum alignment on dissociative chemisorption: Using an improved detection scheme the quadrupole alignment factor A 0 (2) is also obtained as a function of H 2 kinetic energy. These experiments, and the results of the earlier experiments discussed above are compared to results of quantum dynamics calculations using the BOSS model, and employing a PES computed with the SRP functional developed for hydrogen reacting with Cu(111).…”